Metadata for feature classes are not published alongside the map service in ArcGIS GIS Server.

Workaround

1. Export the metadata to an XML file using the FGDC2ESRI_ISO translator and the Export Metadata tool.
2. Stop the service when published, and replace the contents of the metadata XML file in the ArcGIS Server directory, as shown here: DriveLetter:\arcgisserver\config-store\services\ServiceName\esriinfo\metadata

Steps to Reproduce